Controller design for continuous systems with variance and circular pole constraints

The problem of controller design with variance and circular pole constraints is considered in this paper. The motivation for this problem is twofold: (1) many engineering systems have performance requirements naturally stated in terms of upper bounds on the variances of the system states; and (2) the fine transient properties of the closed-loop system are required in practice. The goal of this problem is to design the controller such that the closed-loop system meets the prespecified variance constraints and circular pole constraints simultaneously. It is shown that a desired controller is determined by using the solution of a modified Lyapunov equation. Necessary and sufficient conditions are given for the existence of desired controllers. The set of desired controllers (if they exist) is also characterized.